Laplace Distribution

I am working on Lapalace Distribution with pdf f(x) = (2*beta)^(-1) *
exp(-(absx)/beta). variance of this distribution is 2*(beta^2). so if
we take beta=1/sqrt(2), we have laplace dist'n with unit variance. how
can i write a Mathematica function for this density and how can i plot
the theoretical q-q plot of laplace against Normal.
note. it has to integrate to one.
thanks.
tie@cscn.com